Outlier-robust spectral estimation for spatial lattice processes

Ronit Nirel*, Moira A. Mugglestone, Vic Barnett

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The presence of outliers in spatial data can seriously affect estimates of second-order properties such as auto-covariance functions (ACF's) and spectra. This paper concerns spatial data in the form of continuous measurements on a rectangular grid. We introduce the spatial additive outlier model, which incorporates flexibility to produce both 'isolated' and 'patchy' spatial distributions of outliers. The bias in the ACF and spectrum caused by contamination is analysed, and a non-model-based data-cleaner is proposed. The cleaned data may be used as input to standard routines yielding bias-robust estimates of the required functions. The method compares favourably with other procedures in the absence of contamination and in the presence of isolated outliers. It has an added advantage of being robust to patchy distributions of outliers. Illustrative examples of the application of the method are presented using simulated data and data on the concentration of copper in the soil in UK grid squares.

Original languageAmerican English
Pages (from-to)3095-3111
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Issue number12
StatePublished - 1998

Bibliographical note

Funding Information:
The authors thank Moshe Pollak for most helpful discussions. IACR receives grant-aided support from the Biotechnology and Biological Sciences Research Council of the United Kingdom.


  • Additive outlier
  • Auto-covariance function
  • Fast Fourier transform
  • Min-max
  • Moving-average process
  • Spatial data
  • Two-dimensional spectrum


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